PARAMETER ESTIMATION OF THE MARGINAL CUMULATIVE DISTRIBUTION FUNCTIONS AND OF THE COPULA APPLIED IN HYDROLOGY

Abstract

In this paper we will estimate the parameters of the cumulative distribution functions for marginals for bi-variates and, at the same time, those of the copula that connects them, using a sample of a uniform random variable that depends on these parameters. We will also use the \chi_{1;0.99}^2=9.6349 test for the validation of the model. In fact, the proposed method is a generalization of the PWM (Probability Weighted Moments) method used in literature. For the PWM method there are also used some moments of a uniform random variable, but only for a marginal. In our method we use the uniform random variable for both the marginal and the copula. As an application, we will consider the maximum discharges and the volumes of the floods on the Danube River, connected by a copula in a given gauge station. In this case study, we will estimate the parameters for both the marginal distributions and the copula using the method presented in this paper.

Keywords

• Archimedean copula
• method of the uniform random variable moments
• isolines of exceeding probabilities
• model's validation
• bi-variates
• maximum discharge and volume of the floods